Related papers: Apparent horizons in simplicial Brill wave initial…
Regge calculus is used to construct initial data for vacuum axisymmetric Brill waves at a moment of time symmetry. We argue that only a tetrahedral lattice can successfully reproduce the continuum solution, and develop a simplicial…
A class of analytical solutions of axially symmetric vacuum initial data for a self-gravitating system has been found. The active region of the constructed gravitational wave is a thin torus around which the solution is conformally flat.…
We construct analytical initial data for a slowly moving and rotating black hole for generic orientations of the linear momentum and the spin. We solve the Hamiltonian constraint approximately and work out the properties of the apparent…
We present a series of test beds for numerical codes designed to find apparent horizons. We consider three apparent horizon finders that use different numerical methods: one of them in axisymmetry, and two fully three-dimensional. We…
Apparent horizons are structures of spacelike hypersurfaces that can be determined locally in time. Closed surfaces of constant expansion (CE surfaces) are a generalisation of apparent horizons. I present an efficient method for locating CE…
We establish necessary conditions for the appearance of both apparent horizons and singularities in the initial data of spherically symmetric general relativity when spacetime is foliated extrinsically. When the dominant energy condition is…
We establish sufficient conditions for the appearance of apparent horizons in spherically symmetric initial data when spacetime is foliated extrinsically. Let $M$ and $P$ be respectively the total material energy and the total material…
Black holes in general relativity are characterized by their trapping horizon, a one-way membrane that can be crossed only inwards. The existence of trapping horizons in astrophysical black holes can be tested observationally using a…
Brill waves are the simplest (non-trivial) solutions to the vacuum constraints of general relativity. They are also rich enough in structure to allow us believe that they capture, at least in part, the generic properties of solutions of the…
The requirement that a trapped spacetime domain forms in finite time for distant observers is logically possible and sometimes unavoidable, but its consequences are not yet fully understood. In spherical symmetry, the characterization of…
A major issue in general relativity and blackhole physics today is to determine the conditions when the spacetime singularities forming as end-states of gravitational collapse are visible to external observers, and when these are hidden…
The pseudospectral code bamps is used to evolve axisymmetric gravitational waves. We consider a one-parameter family of Brill wave initial data, taking the seed function and strength parameter of Holz et. al. A careful comparison is made to…
For finite abstract simplicial complex $\Sigma$, initial realization $\alpha$ in $\mathbb{E}^d$, and desired edge lengths $L$, we give practical sufficient conditions for the existence of a non-self-intersecting perturbation of $\alpha$…
We report the development of the first apparent horizon locator capable of finding multiple apparent horizons in a ``generic'' numerical black hole spacetime. We use a level-flow method which, starting from a single arbitrary initial trial…
Fine-tuning generic but smooth spherically-symmetric initial data for general relativity to the threshold of dynamical black hole formation creates arbitrarily large curvatures, mediated by a universal self-similar solution that acts as an…
Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…
We present the first results in a new program intended to make the best use of all available technologies to provide an effective understanding of waves from inspiralling black hole binaries in time for imminent observations. In particular,…
Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial…
We study critical black hole separations for the formation of a common apparent horizon in systems of $N$ - black holes in a time symmetric configuration. We study in detail the aligned equal mass cases for $N=2,3,4,5$, and relate them to…
Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon -- weak cosmic censorship conjecture -- and ii) spacetime eventually settles down to a…